The term multiple alleles means that even though each individual in a population gets two alleles for a trait, more than two different alleles are present in the population's genes.
One example of multiple alleles are Blood Groups
The blood types of the ABO system are determined by cell-surface antigens, Antigens are large molecules that are capable of reacting with specific antibodies. In terms of dominance, IA and IB are codominant, and both are dominant over IO. IA, IB, and IO are multiple alleles.
From the alleles IA, IB, and IO there are six possible genotypes. From these six genotypes there are only four blood groups or phenotypes (A, B, AB, and O).
The immune systems of individuals produce either anti-A or anti-B antibodies. The type A person produces anti-B, type B produces anti-A, type AB produces neither, and type O produces both.
When antibodies meet opposing antigens on red cell surfaces, they bind to these and form bridges to other red cells nearby. The massive binding of these cells is called agglutination, or clumping.
Because of antigen-antibody reactions, blood transfusions have to be preceded by careful blood-matching tests. The antigens on the surface of our red blood cells are carbohydrates (attached to proteins embedded in the cell membrane -glycoproteins actually). Exposure to dietary carbohydrates, which are known to be similar to those found on erythrocytes, may prepare the immune system in advance of a transfusion.
Rh blood groups can be divided into Rh positive and Rh negative -- several antigens are involved. In blood transfusions, this factor must be considered along with the ABO factors.
Rh antibodies are only present when a person receives Rh+ antigens. The presence of antigen induces an immune reaction, and the antibodies are produced.
The immune reaction of Rh- people to Rh+ antigens extends into reproduction. Rh+ fathers can pass the antigen-producing gene to their offspring. When Rh- mothers bear Rh+ children, there can be mixing of maternal and fetal blood, causing the mother to produce antibodies. Subsequent pregnancies are potentially dangerous, since the antibodies can enter the fetal blood and cause agglutination. The immune response can be clinically suppressed if the incompatibility is known.
A wealth of data now revelas that hemolytic disease can be caused by unfavorable antigenic mother-child interactions involving the ABO blood groups as well. Anti-A and anti-B antibodies produce their injurious effects primarily in early pregnancy resulting in spontaneous abortions among type O women married to type A or B men. (Type O blood is rather rare -- is there any question why in light of this evidence?)
Human's also have other carbohydrates studding the surface of red blood cells. This site discusses the M and N blood types.